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An Introduction To Non-aristotelian Systems And General Semantics.

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750
SUPPLEMENT III
the possible form and matter of all that does not exist, but might. As far as it could be done, it would give the grand Cyclopaedia, and its yearly supplement would be the history of the human race for the time', said Augustus de Morgan in his Formal Logic, and this opinion I found fully justified.
So I must be brief, and state but roughly, that in the Indo-european languages the verb 'to be' has at least four entirely different uses: (1) as an auxiliary verb, 'Smith is coming'; (2) as the 'is' of predication, 'the apple is red'; (3) as the 'is' of 'existence', 'I am'; (4) as the 'is' of identity, 'the apple is a fruit'. The fact that four semantically entirely different words should have one sound and spelling appears as a genuine tragedy of the race; the more so since the discrimination between their uses is not always easy.
The researches of the present writer have shown that the problems involved are very complicated and cannot be solved except by a joint study of mathematics, mathematical foundations, history of mathematics, 'logic', 'psychology', anthropology, psychiatry, linguistics, epistemology, physics and its history, colloidal chemistry, physiology, and neurology; this study resulting in the discovery of a general semantic mechanism underlying human behaviour, many new interrelations and formulations, culminating in a -system. This semantic mechanism appears as a general psychophysiological mechanism based on four-dimensional order, present and abused in all of us, the primitive man, the infant, the 'mentally' ill, and the genius not excluded. It gives us an extremely simple means of training our s.r, which can be applied even in elementary education.
The scientific problems involved are very extensive and can be dealt with only in a large volume. Here I am able to give only a very sketchy summary without empirical data, omit ting niceties and technicalities.
If we consider an actual territory (a) say, Paris, Dresden, Warsaw, and build up a map (b) in which the order of these cities would be represented as Dresden, Paris, Warsaw; to travel by such a map would be misguiding, wasteful of effort, . In case of emergencies, it might be seriously harmful, . We could say that such a map was 'not true'. , or that the map had a structure not similar to the territory, structure to be defined in terms of relations and multidimensional order. We should notice that:
A)  A map may have a structure similar or dissimilar to the structure of the territory.                                                                                                 (1)
B)  Two similar structures have similar 'logical' characteristics. Thus, if in a correct map, Dresden is given as between Paris and Warsaw, a similar relation is found in the actual territory.                                                         (2)
C)  A map is not the territory.                                                                   (3)